Ibrahimovic felt Sweden produced a vastly improved display compared to when beaten 2-1 by Ukraine in their opening game. But they again surrendered the advantage when in front and have nothing but pride to play for in their final fixture against Group D leaders France on Tuesday.
Ibrahimovic told UEFA.com: "I think we were the better team against England. I really do. We should be proud of ourselves because we played a good game. We played the opposite way to the first one. We showed more courage and were much better in dead-ball situations. We played just the way we wanted to play.
"But in both the games we have played, we were in the lead, but after 60 minutes, we lost it all. Why did we lose both games? I don't know. That is something we need to analyse and see what we need to do better, or in a different way."
Midfielder Sebastian Larsson echoed Ibrahimovic's sentiments. He said: "We did not play a good first match [against Ukraine] even if we should have taken points. Against England, it feels like we were the best team, but it isn't always the best team that wins.
"It is about taking points, and we didn't do that. It doesn't really matter now we are out of the tournament, but we were definitely better than England, but they are leaving with the points, so what can you say?
"Their equaliser [from Theo Walcott] happens one time in a thousand. It was a shot I should have covered and it hit me and deflected past the goalkeeper.
"With the last goal [from Danny Welbeck] it's one player against four of ours, like with the goals against Ukraine, so it is things like that which decide the outcome. We have not done well enough."